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   "cell_type": "markdown",
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   "source": [
    "# 第二回：艺术画笔见乾坤\n",
    "\n",
    "主要了解 matplotlib 中\n",
    "- primitives\n",
    "- container\n",
    "\n",
    "## 一、概述\n",
    "\n",
    "### 1. Matplotlib 的三层 API\n",
    "\n",
    "与画家作画的步骤类似：\n",
    "\n",
    "1. 准备一块 **画布**（<font style=\"color:rgba(232, 62, 140, 1);text-decoration:none;\">matplotlib.backend_bases.FigureCanvasBase</font>）；\n",
    "2. 准备好 **颜料和画笔** 等工具，即组件（<a href=\"https://matplotlib.org/stable/api/artist_api.html#matplotlib.artist.Artist\" style=\"color:rgba(232, 62, 140, 1);\">matplotlib.artist.Artist</a>）；\n",
    "3. 使用占有颜料的画笔在画布上 **作画** ，即渲染（<font style=\"color:rgba(232, 62, 140, 1);text-decoration:none;\">matplotlib.backend_bases.RendererBase</font>）；\n",
    "\n",
    "<a href=\"https://matplotlib.org/stable/api/artist_api.html#matplotlib.artist.Artist\" style=\"color:rgba(232, 62, 140, 1);\">Artist</a> 代表了具体的**图表组件**，即调用了 <font style=\"color:rgba(232, 62, 140, 1);text-decoration:none;\">Render</font> 的接口在 <font style=\"color:rgba(232, 62, 140, 1);text-decoration:none;\">FigureCanvas</font> 上作图。\n",
    "<font style=\"color:rgba(232, 62, 140, 1);text-decoration:none;\">FigureCanvas</font> 和 <font style=\"color:rgba(232, 62, 140, 1);text-decoration:none;\">Render</font> 处理程序和计算机的底层交互的事项，<a href=\"https://matplotlib.org/stable/api/artist_api.html#matplotlib.artist.Artist\" style=\"color:rgba(232, 62, 140, 1);\">Artist</a> 是具体的调用接口，比如图形、文本、线条的设定，这可以做出我们想要的图。\n",
    "\n",
    "我们95%的时间，都不需要关注 <font style=\"color:rgba(232, 62, 140, 1);text-decoration:none;\">FigureCanvas</font> 和 <font style=\"color:rgba(232, 62, 140, 1);text-decoration:none;\">Render</font>，而只与 <a href=\"https://matplotlib.org/stable/api/artist_api.html#matplotlib.artist.Artist\" style=\"color:rgba(232, 62, 140, 1);\">Artist</a> 打交道即可。"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### 2. Artist的分类\n",
    "\n",
    "<img src=\"https://ai-studio-static-online.cdn.bcebos.com/7e8e042150c241c392db9cb43a6ac4a54b776237e881411aaa4dffe19673d8a4\" style=\"zoom:50%;\"><br/><br/>\n",
    "\n",
    "artist 大致分为 `primitives`(基本元素) 和 `containers`(容器) 两个部分。\n",
    "- `primitives`\n",
    "    - lines: 线, 主要是 <a href=\"https://matplotlib.org/stable/api/_as_gen/matplotlib.lines.Line2D.html#matplotlib.lines.Line2D\" style=\"color:rgba(232, 62, 140, 1);\">matplotlib.lines.Line2D</a>;\n",
    "    - text: 文本, 有 <a href=\"https://matplotlib.org/stable/api/text_api.html#matplotlib.text.Annotation\" style=\"color:rgba(232, 62, 140, 1);\">matplotlib.text.Annotation</a>, <a href=\"https://matplotlib.org/stable/api/text_api.html#matplotlib.text.Text\" style=\"color:rgba(232, 62, 140, 1);\">matplotlib.text.Text</a> 两个;\n",
    "    - rectangle: 矩形，<a href=\"https://matplotlib.org/stable/api/_as_gen/matplotlib.patches.Rectangle.html#matplotlib.patches.Rectangle\" style=\"color:rgba(232, 62, 140, 1);\">matplotlib.patches.Rectangle</a>;\n",
    "    - image: 图像, <a href=\"https://matplotlib.org/stable/api/image_api.html#matplotlib.image.AxesImage\" style=\"color:rgba(232, 62, 140, 1);\">matplotlib.image.AxesImage</a>;\n",
    "- `containers`\n",
    "    - figure: 图表, <a href=\"https://matplotlib.org/stable/api/axes_api.html#matplotlib.figure.Figure\" style=\"color:rgba(232, 62, 140, 1);\">matplotlib.figure.Figure</a>;\n",
    "    - axes: 坐标系, <a href=\"https://matplotlib.org/stable/api/axes_api.html#matplotlib.axes.Axes\" style=\"color:rgba(232, 62, 140, 1);\">matplotlib.axes.Axes</a>;\n",
    "    - axis: 坐标轴, <a href=\"https://matplotlib.org/stable/api/axis_api.html#matplotlib.axis.Axis\" style=\"color:rgba(232, 62, 140, 1);\">matplotlib.axis.Axis</a>;\n",
    "\n",
    "\n",
    "最外层的 container 是 `Figure`，里面有一个或多个 `Axes`。而 `Axes` 又是一个小容器，每个` Axes` 包含 title、label、Axis 等元素。如下图所示。\n",
    "    \n",
    "<img src=\"https://ai-studio-static-online.cdn.bcebos.com/d5969919aa844a118706e9b9e1f218194533a89fee7644c4996e880df3ca0268\" style=\"zoom:50%;\">"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### 3. Matplotlib 标准用法\n",
    "\n",
    "**三个步骤**：\n",
    "\n",
    "<img src=\"https://ai-studio-static-online.cdn.bcebos.com/d40aa9ad9b6d49c4ba7085b161e3b03529090ba171744277966416865964157a\" style=\"zoom:10%;\"><br/><br/>\n",
    "\n",
    "`Axes` 这个容器上面有很多常用的字段属性和方法，如，对于作图十分重要，因此我们需要重点学习它。"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "!mkdir /home/aistudio/external-libraries\n",
    "!pip install beautifulsoup4 -t /home/aistudio/external-libraries"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "!pip install --upgrade matplotlib"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {
    "execution": {
     "iopub.execute_input": "2021-11-23T08:36:14.173337Z",
     "iopub.status.busy": "2021-11-23T08:36:14.172816Z",
     "iopub.status.idle": "2021-11-23T08:36:16.225112Z",
     "shell.execute_reply": "2021-11-23T08:36:16.224314Z",
     "shell.execute_reply.started": "2021-11-23T08:36:14.173300Z"
    }
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "python version: 3.7.4 (default, Aug 13 2019, 20:35:49) \n",
      "[GCC 7.3.0]\n",
      "matplotlib version: 3.5.0\n"
     ]
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      "text/plain": [
       "<Figure size 432x288 with 2 Axes>"
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     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "%config InlineBackend.figure_format = 'svg'  # 显示矢量图\n",
    "import sys\n",
    "sys.path.append('/home/aistudio/external-libraries')\n",
    "import matplotlib as mpl\n",
    "import matplotlib.pyplot as plt\n",
    "import numpy as np\n",
    "print(f\"python version: {sys.version}\")\n",
    "print(f\"matplotlib version: {mpl.__version__}\")\n",
    "\n",
    "# 1. 通过 `plt.figure()` 实例化 `Figure`\n",
    "fig = plt.figure()\n",
    "\n",
    "# 2. 利用 `fig` 创建了一个两行一列(即可以有两个`subfigure` )的绘图区，并同时在第一个位置创建了一个 `SubFigure` 实例\n",
    "ax1 = fig.add_subplot(2, 1, 1) # two rows, one column, first plot\n",
    "\n",
    "# 3. 利用 `Axes` 实例的方法画了一条曲线\n",
    "t = np.arange(0.0, 1.0, 0.01)\n",
    "s1 = np.sinc(2*np.pi*t)\n",
    "s2 = np.sinc(2*2*np.pi*t)\n",
    "line, = ax1.plot(t, s1, color='orange', lw=2, ls='--')\n",
    "ax1.set_title(\"ax1_title\")\n",
    "\n",
    "ax2 = fig.add_subplot(2, 1, 2) # two rows, one column, first plot\n",
    "line2, = ax2.plot(t, s2, color='skyblue', lw=2, ls='-.')\n",
    "ax2.set_title(\"ax2_title\")\n",
    "\n",
    "fig.suptitle('super title')\n",
    "# fig.tight_layout()\n",
    "\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "# 颜色名如下\n",
    "import matplotlib.colors as mcolors\n",
    "print(list(mcolors.BASE_COLORS.keys()), end='\\n\\n')\n",
    "print(list(mcolors.TABLEAU_COLORS.keys()), end='\\n\\n')\n",
    "print(list(mcolors.CSS4_COLORS.keys()), end='\\n\\n')\n",
    "print(list(mcolors.XKCD_COLORS.keys()))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## 二、基本元素 `primitives`\n",
    "\n",
    "`primitives` 分为：\n",
    "- 折线 -`Line2D`\n",
    "- 矩形 -`Rectangle`\n",
    "- 图像 -`image`\n",
    "- 文本 -`Text`\n",
    "\n",
    "### 1. lines\n",
    "\n",
    "通过 [`class matplotlib.lines.Line2D`](https://matplotlib.org/stable/api/_as_gen/matplotlib.lines.Line2D.html#matplotlib.lines.Line2D) 可以完成折线的绘制。\n",
    "\n",
    "`Line2D`: 线既可以有连接所有顶点的实线样式，也可以在每个顶点处有一个标记。构造函数如下：\n",
    "\n",
    "```python\n",
    "def __init__(self, \n",
    "    xdata,            # array, x轴数据\n",
    "    ydata,            # array, y轴数据\n",
    "    linewidth=None,   # float, 线的宽度\n",
    "    linestyle=None,   # string, 线的样式\n",
    "    color=None,       # string, 线的颜色，可以是已有的颜色名或RGB或HEX\n",
    "    marker=None,      # string，线的标记\n",
    "    markersize=None,  # float，标记的大小\n",
    "    markeredgewidth=None, # float，标记边缘的宽度\n",
    "    markeredgecolor=None, # string，标记边缘的颜色\n",
    "    markerfacecolor=None, # string，标记面的颜色\n",
    "    ...)\n",
    "```\n",
    "\n",
    "\n",
    "`marker`: 在 <a href=\"https://matplotlib.org/stable/api/markers_api.html#module-matplotlib.markers\" style=\"color:rgba(232, 62, 140, 1);\">matplotlib.markers</a> 有详细介绍，我们可以通过 `Line2D.markers` 和`Line2D.filled_markers` 查看信息。也可以使用 MathText，使用自定义标记符号。"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "**有三种方法可以用设置线的属性**：\n",
    "\n",
    "\n",
    "1. 通过获得线对象，对线对象进行设置\n",
    "\n",
    "    `matplotlib.lines.Line2D` 对象有很多 setter 方法，可以设置线对象的属性，参考 [Line2D API](https://matplotlib.org/stable/api/_as_gen/matplotlib.lines.Line2D.html)\n",
    "\n",
    "2. 直接在 `pyplot.plot()`/`axes.plot()` 函数中设置，实际上这和第一种方法一样，只是做了一些封装。\n",
    "\n",
    "```python\n",
    "# plt.plot() --> Axes.plot() --> _process_plot_var_args._makeline()\n",
    "\n",
    "# _process_plot_var_args._makeline()核心逻辑代码\n",
    "def _makeline(self, x, y, kw, kwargs):\n",
    "    kw = {**kw, **kwargs}\n",
    "    # 通过Line2D的构造方法创建实例对象，kw是我们为线对象设置的属性\n",
    "    seg = mlines.Line2D(x, y, **kw)\n",
    "    return seg, kw\n",
    "```\n",
    "\n",
    "\n",
    "3. 获得线属性，使用 `pyplot.setp()` 函数设置，实际上是通过 `getattr()` 获取`setter`方法来设置`Line2D` 的属性，这还是与第一种方法一样。\n",
    "\n",
    "\n",
    "```python\n",
    "# pyplot.setp() --> artist.Artist.setp() --> artist.Artist.set() --> artist.Artist.update()\n",
    "\n",
    "# 下面是update()的核心逻辑代码\n",
    "def update(self, props):\n",
    "    for k, v in props.items():\n",
    "        func = getattr(self, f\"set_{k}\", None)\n",
    "        ret.append(func(v))\n",
    "    return ret\n",
    "```"
   ]
  },
  {
   "cell_type": "code",
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     "iopub.status.busy": "2021-11-21T15:37:09.589887Z",
     "iopub.status.idle": "2021-11-21T15:37:09.743169Z",
     "shell.execute_reply": "2021-11-21T15:37:09.742633Z",
     "shell.execute_reply.started": "2021-11-21T15:37:09.590422Z"
    }
   },
   "outputs": [
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      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "import matplotlib as mpl\n",
    "import matplotlib.pyplot as plt\n",
    "import numpy as np\n",
    "# 方式1：通过获得线对象，对线对象进行设置\n",
    "x = np.linspace(-10.0, 10.0, 100)\n",
    "y = np.exp(-x**2/2)\n",
    "\n",
    "ax = plt.subplot(111)\n",
    "ax.spines['right'].set_color('none')\n",
    "ax.spines['top'].set_color('none')\n",
    "ax.xaxis.set_ticks_position('bottom')\n",
    "ax.spines['bottom'].set_position(('data', 0))\n",
    "ax.yaxis.set_ticks_position('left')\n",
    "ax.spines['left'].set_position(('data',0))\n",
    "\n",
    "line, = ax.plot(x, y)\n",
    "line.set_color(plt.cm.rainbow(0.1))\n",
    "line.set_linestyle(\"--\")\n",
    "line.set_linewidth(2.5)\n",
    "\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 55,
   "metadata": {
    "execution": {
     "iopub.execute_input": "2021-11-21T15:37:06.319292Z",
     "iopub.status.busy": "2021-11-21T15:37:06.318551Z",
     "iopub.status.idle": "2021-11-21T15:37:06.469432Z",
     "shell.execute_reply": "2021-11-21T15:37:06.468677Z",
     "shell.execute_reply.started": "2021-11-21T15:37:06.319259Z"
    }
   },
   "outputs": [
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      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# 方式2：直接在 `pyplot.plot()`/`axes.plot()` 函数中设置\n",
    "x = np.linspace(-10.0, 10.0, 100)\n",
    "y = np.exp(-x**2/2)\n",
    "\n",
    "ax = plt.subplot(111)\n",
    "ax.spines['right'].set_color('none')\n",
    "ax.spines['top'].set_color('none')\n",
    "ax.xaxis.set_ticks_position('bottom')\n",
    "ax.spines['bottom'].set_position(('data', 0))\n",
    "ax.yaxis.set_ticks_position('left')\n",
    "ax.spines['left'].set_position(('data',0))\n",
    "\n",
    "line, = ax.plot(x, y, marker='s', color=plt.cm.rainbow(0.4), linewidth=2.5)\n",
    "\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 54,
   "metadata": {
    "execution": {
     "iopub.execute_input": "2021-11-21T15:37:02.182391Z",
     "iopub.status.busy": "2021-11-21T15:37:02.181546Z",
     "iopub.status.idle": "2021-11-21T15:37:02.349142Z",
     "shell.execute_reply": "2021-11-21T15:37:02.348577Z",
     "shell.execute_reply.started": "2021-11-21T15:37:02.182333Z"
    }
   },
   "outputs": [
    {
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      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# 方式3：获得线属性，使用 `pyplot.setp()` 函数设置\n",
    "x = np.linspace(-10.0, 10.0, 100)\n",
    "y = np.exp(-x**2/2)\n",
    "\n",
    "ax = plt.subplot(111)\n",
    "ax.spines['right'].set_color('none')\n",
    "ax.spines['top'].set_color('none')\n",
    "ax.xaxis.set_ticks_position('bottom')\n",
    "ax.spines['bottom'].set_position(('data', 0))\n",
    "ax.yaxis.set_ticks_position('left')\n",
    "ax.spines['left'].set_position(('data',0))\n",
    "\n",
    "line, = ax.plot(x, y)\n",
    "plt.setp(line, color=plt.cm.rainbow(0.7), alpha=0.9)\n",
    "plt.setp(line, linewidth=3)\n",
    "plt.setp(line, marker='8', markersize=8.0, markerfacecolor=plt.cm.rainbow(0.84), markeredgecolor=plt.cm.rainbow(0.7), markeredgewidth=1.2)\n",
    "\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "线图有两种分类：普通线图，误差线图\n",
    "\n",
    "#### 1.1 普通线图\n",
    "\n",
    "**绘制直线line常用的方法有两种**:\n",
    "\n",
    "1. `pyplot` 方法绘制\n",
    "\n",
    "2. `Line2D` 对象绘制"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 53,
   "metadata": {
    "execution": {
     "iopub.execute_input": "2021-11-21T15:36:59.075400Z",
     "iopub.status.busy": "2021-11-21T15:36:59.074391Z",
     "iopub.status.idle": "2021-11-21T15:36:59.189710Z",
     "shell.execute_reply": "2021-11-21T15:36:59.189057Z",
     "shell.execute_reply.started": "2021-11-21T15:36:59.075362Z"
    }
   },
   "outputs": [
    {
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      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# 方法1：`pyplot` 方法绘制\n",
    "x = range(1,11)\n",
    "y = np.random.randn(10)\n",
    "plt.plot(x, y, marker='o', markerfacecolor=plt.cm.Oranges(0.8), markersize=10, color=plt.cm.Oranges(0.45), linewidth=4)\n",
    "\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 52,
   "metadata": {
    "execution": {
     "iopub.execute_input": "2021-11-21T15:36:55.162895Z",
     "iopub.status.busy": "2021-11-21T15:36:55.162377Z",
     "iopub.status.idle": "2021-11-21T15:36:55.306035Z",
     "shell.execute_reply": "2021-11-21T15:36:55.303548Z",
     "shell.execute_reply.started": "2021-11-21T15:36:55.162859Z"
    }
   },
   "outputs": [
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      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# 方法2: `Line2D` 对象绘制\n",
    "x = np.linspace(0.0, 5.0, 10)\n",
    "y = np.random.uniform(low=0.0, high=5.0, size=10)\n",
    "line, = plt.plot(x, y)\n",
    "line.set_marker(\"h\")\n",
    "line.set_markersize(10)\n",
    "line.set_markerfacecolor(plt.cm.viridis(0.5))\n",
    "line.set_color(plt.cm.viridis(0.8))\n",
    "line.set_linewidth(4.0)\n",
    "\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "execution": {
     "iopub.execute_input": "2021-11-17T13:39:14.414341Z",
     "iopub.status.busy": "2021-11-17T13:39:14.413300Z",
     "iopub.status.idle": "2021-11-17T13:39:14.420148Z",
     "shell.execute_reply": "2021-11-17T13:39:14.419401Z",
     "shell.execute_reply.started": "2021-11-17T13:39:14.414300Z"
    }
   },
   "source": [
    "#### 1.2 误差线图\n",
    "\n",
    "\n",
    "1. `matplotlib.container.ErrorbarContainer`\n",
    "\n",
    "\n",
    "2.  `pyplot.errorbar`/ `Axes.errorbar`\n",
    "\n",
    "```python\n",
    "# matplotlib.axes.Axes.errorbar() --> matplotlib.container.ErrorbarContainer\n",
    "def errorbar(self, \n",
    "             x, y,                  # array-like, 与绘制普通折线图的数据一样\n",
    "             yerr=None, xerr=None,  # array-like, 误差数据\n",
    "             fmt='',                # string, 与plot中的一样\n",
    "             ecolor=None,           # string, 误差线的颜色\n",
    "             elinewidth=None,       # float, 误差线的宽度\n",
    "             capsize=None,          # float, 误差线的长度\n",
    "             barsabove=False,       # bool, False表示误差线在折线的下面，Fure表示误差线在折线的上面。\n",
    "             lolims=False, uplims=False, xlolims=False, xuplims=False, \n",
    "             errorevery=1, capthick=None, **kwargs):\n",
    "    # ...\n",
    "    self._request_autoscale_view()\n",
    "    errorbar_container = ErrorbarContainer(\n",
    "        (data_line, tuple(caplines), tuple(barcols)),\n",
    "        has_xerr=(xerr is not None), has_yerr=(yerr is not None),\n",
    "        label=label)\n",
    "    self.containers.append(errorbar_container)\n",
    "    return errorbar_container\n",
    "```"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 51,
   "metadata": {
    "execution": {
     "iopub.execute_input": "2021-11-21T15:36:50.934583Z",
     "iopub.status.busy": "2021-11-21T15:36:50.933580Z",
     "iopub.status.idle": "2021-11-21T15:36:51.081355Z",
     "shell.execute_reply": "2021-11-21T15:36:51.080423Z",
     "shell.execute_reply.started": "2021-11-21T15:36:50.934549Z"
    }
   },
   "outputs": [
    {
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      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "import matplotlib as mpl\n",
    "import matplotlib.pyplot as plt\n",
    "import numpy as np\n",
    "\n",
    "x = np.linspace(0.1, 0.5*np.pi, 10)\n",
    "y = 2.5 * np.sinc(np.pi*x)\n",
    "yerr = 0.3 * np.random.normal(scale=0.5, size=10)\n",
    "\n",
    "fig = plt.figure()\n",
    "ax = fig.add_subplot()\n",
    "ax.errorbar(x, y, yerr=yerr, color=plt.cm.viridis(0.8), lw=3.0, ecolor=plt.cm.viridis(0.45), elinewidth=3.0, barsabove=True)\n",
    "\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### 2. patches\n",
    "\n",
    "<img src=\"https://matplotlib.org/stable/_images/inheritance-ecef1d6fc5ffec0460463869049eb0c708a450cc.png\" style=\"zoom:0.6;\">\n",
    "\n",
    "patches 是 artist 中的面颜色（face color）和轮廓颜色（edge color）。paches中基类是 [`Patch`](https://matplotlib.org/stable/api/_as_gen/matplotlib.patches.Patch.html#matplotlib.patches.Patch)，构造函数如下：\n",
    "\n",
    "```python\n",
    "def __init__(self,\n",
    "    edgecolor=None,    # string, ec, 边缘轮廓颜色\n",
    "    facecolor=None,    # string, fc, 面颜色\n",
    "    color=None,        # string, c, 同时设置 edgecolor and facecolor\n",
    "    linewidth=None,    # float, lw, patch linewidth\n",
    "    linestyle=None,    # string, ls, patch linestyle\n",
    "    antialiased=None,  # bool, aa, 设置是否使用抗锯齿的渲染方式\n",
    "    hatch=None,        # string, 设置填充图案, {'/', '\\', '|', '-', '+', 'x', 'o', 'O', '.', '*'}\n",
    "    fill=True,         # bool, 设置是否填充 patch.\n",
    "    capstyle=None,     # string, 设置绘制未闭合线的两个端点（端点）, CapStyle or {'butt', 'projecting', 'round'}\n",
    "    joinstyle=None,    # string, 绘制两条线段之间的连接, JoinStyle or {'miter', 'round', 'bevel'}\n",
    "    **kwargs):\n",
    "```"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### 2.1 Rectangle 矩形\n",
    "\n",
    "通过锚点 xy 和 宽高 定义矩形。\n",
    "```plain\n",
    "  +------------------+\n",
    "  |                  |\n",
    " 高                  |\n",
    "  |                  |\n",
    " (xy)----- 宽 -------+\n",
    "```\n",
    "构造函数如下：\n",
    "\n",
    "```python\n",
    "# matplotlib.patches.Rectangle\n",
    "def __init__(self, \n",
    "             xy,         # (float, float), 锚点的位置\n",
    "             width,      # float, 矩形的宽度\n",
    "             height,     # float, 矩形的高度\n",
    "             angle=0.0,  # float, 绕锚点xy逆时针旋转的角度\n",
    "             **kwargs)\n",
    "```\n"
   ]
  },
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      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "import matplotlib.pyplot as plt\n",
    "import matplotlib.patches as mpatches\n",
    "plt.rcdefaults()\n",
    "def pick_rec(artist, mouseevent):\n",
    "    rect.set_color(\"orange\")\n",
    "    return False, 1 \n",
    "\n",
    "fig = plt.figure()\n",
    "ax = fig.add_subplot(111)\n",
    "\n",
    "# 创建Rectangle实例对象\n",
    "rect = mpatches.Rectangle(xy=(0.1, 0.1), width=0.2, height=0.6)\n",
    "ax.add_patch(rect)\n",
    "\n",
    "# 设置pick事件\n",
    "rect.set_picker(pick_rec)\n",
    "\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "由矩形组成的图有两种：\n",
    "\n",
    "1. 条形图: `Axes.bar()` / `Axes.barh()`\n",
    "\n",
    "```python\n",
    "Axes.bar(x, height, width=0.8, bottom=None, *, align='center', data=None, **kwargs)\n",
    "```\n",
    "\n",
    "```python\n",
    "# matplotlib.axes.Axes.bar\n",
    "def bar(self, \n",
    "        x,              # float or array-like, 条形的 x 坐标\n",
    "        height,         # float or array-like, 条形的高度\n",
    "        width=0.8,      # float or array-like, 条形的宽度\n",
    "        bottom=None,    # float or array-like, 条形底座的 y 坐标。\n",
    "        *, \n",
    "        align=\"center\", # string, 条形与 x 坐标的对齐方式，\n",
    "        # {'center', 'edge'}, 'center'代表条形以 x 位置为中心，'edge'代表条形的左边缘与 x 位置对齐\n",
    "        **kwargs):\n",
    "    # ...\n",
    "    args = zip(left, bottom, width, height, color, edgecolor, linewidth, hatch)\n",
    "    # 创建多个 Rectangle，并设置其属性\n",
    "    for l, b, w, h, c, e, lw, htch in args:\n",
    "        r = mpatches.Rectangle(\n",
    "            xy=(l, b), width=w, height=h,\n",
    "            facecolor=c,\n",
    "            edgecolor=e,\n",
    "            linewidth=lw,\n",
    "            label='_nolegend_',\n",
    "            hatch=htch,\n",
    "            )\n",
    "        r.update(kwargs)\n",
    "        r.get_path()._interpolation_steps = 100\n",
    "        if orientation == 'vertical':\n",
    "            r.sticky_edges.y.append(b)\n",
    "        elif orientation == 'horizontal':\n",
    "            r.sticky_edges.x.append(l)\n",
    "        self.add_patch(r)\n",
    "        patches.append(r)\n",
    "    # ...\n",
    "    # 创建 BarContainer\n",
    "    bar_container = BarContainer(patches, errorbar, datavalues=datavalues, orientation=orientation, label=label)\n",
    "    self.add_container(bar_container)\n",
    "    # ...\n",
    "    return bar_container\n",
    "```\n",
    "\n",
    "\n",
    "2. 频率直方图: `Axes.hist()`\n",
    "\n",
    "```python\n",
    "# matplotlib.axes._axes.Axes.hist\n",
    "def hist(self, \n",
    "         x,                   # array \n",
    "         bins=None,           # int or sequence, default: 10\n",
    "         range=None,          # tuple or None，default: None\n",
    "         density=False,       # bool, default: False\n",
    "         weights=None,        # array-like or None, default: None\n",
    "         cumulative=False,    # bool or -1, default: False\n",
    "         bottom=None,         # array-like, scalar, or None, default: None\n",
    "         histtype='bar',      # str, {'bar', 'barstacked', 'step', 'stepfilled'}, default: 'bar'\n",
    "         align='mid', \n",
    "         orientation='vertical', \n",
    "         rwidth=None, \n",
    "         log=False, \n",
    "         color=None, \n",
    "         label=None, \n",
    "         stacked=False, \n",
    "         **kwargs):\n",
    "    # ...\n",
    "    # 通过 _barfunc() 函数创建 bars\n",
    "    for m, c in zip(tops, color):\n",
    "        if bottom is None:\n",
    "            bottom = np.zeros(len(m))\n",
    "        if stacked:\n",
    "            height = m - bottom\n",
    "        else:\n",
    "            height = m\n",
    "        bars = _barfunc(bins[:-1]+boffset, height, width,\n",
    "                        align='center', log=log,\n",
    "                        color=c, **{bottom_kwarg: bottom})\n",
    "        patches.append(bars)\n",
    "    # ...\n",
    "    # 设置 pathces的属性\n",
    "    for patch, lbl in itertools.zip_longest(patches, labels):\n",
    "        if patch:\n",
    "            p = patch[0]\n",
    "            p.update(kwargs)\n",
    "            if lbl is not None:\n",
    "                p.set_label(lbl)\n",
    "            for p in patch[1:]:\n",
    "                p.update(kwargs)\n",
    "                p.set_label('_nolegend_')\n",
    "    # ...\n",
    "    # 返回结果\n",
    "    if nx == 1:\n",
    "        return tops[0], bins, patches[0]\n",
    "    else:\n",
    "        patch_type = (\"BarContainer\" if histtype.startswith(\"bar\")\n",
    "                      else \"list[Polygon]\")\n",
    "        return tops, bins, cbook.silent_list(patch_type, patches)\n",
    "\n",
    "```\n",
    "\n",
    "3. Rectangle 矩形类绘制直方图\n",
    "\n",
    "\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 46,
   "metadata": {
    "execution": {
     "iopub.execute_input": "2021-11-21T15:34:28.723419Z",
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     "shell.execute_reply.started": "2021-11-21T15:34:28.723382Z"
    }
   },
   "outputs": [],
   "source": [
    "import json\n",
    "import requests\n",
    "import pandas as pd\n",
    "from IPython.core.display import HTML\n",
    "\n",
    "url = 'https://api.bilibili.com/pgc/season/index/result?'\\\n",
    "        +'season_version=-1&spoken_language_type=-1&area=-1'\\\n",
    "        +'&is_finish=-1&copyright=-1&season_status=-1&season_month=-1'\\\n",
    "        +'&year=-1&style_id=-1&order=3&st=1&sort=0&page=1&season_type=1&pagesize=20&type=1'\n",
    "html = requests.get(url).text\n",
    "html = json.loads(html)[\"data\"]\n",
    "\n",
    "title_list, order_list = [], []\n",
    "for item in html[\"list\"]:\n",
    "    title_list.append(item[\"title\"])\n",
    "    order_list.append(float(item[\"order\"][:-3]))\n",
    "data = pd.DataFrame({\"title\": title_list , \"order\": order_list})\n",
    "data.sort_values(by=\"order\", axis=0, ascending=True, inplace=True)  # 按追番人数升序排列\n",
    "data.index = range(len(data))\n",
    "tbl_md = data.to_markdown()\n",
    "# print(tbl_md)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "|    | title                                        |   order |\n",
    "|---:|:---------------------------------------------|--------:|\n",
    "|  0 | 欢迎来到实力至上主义的教室                   |   678.1 |\n",
    "|  1 | 埃罗芒阿老师                                 |   684.7 |\n",
    "|  2 | 关于我转生变成史莱姆这档事                   |   708.8 |\n",
    "|  3 | 青春猪头少年不会梦到兔女郎学姐               |   709.1 |\n",
    "|  4 | 紫罗兰永恒花园                               |   711.7 |\n",
    "|  5 | 辉夜大小姐想让我告白～天才们的恋爱头脑战～   |   714.5 |\n",
    "|  6 | 辉夜大小姐想让我告白？～天才们的恋爱头脑战～ |   737.2 |\n",
    "|  7 | 小林家的龙女仆                               |   754.5 |\n",
    "|  8 | Re：从零开始的异世界生活 第二季 前半         |   765.3 |\n",
    "|  9 | 鬼灭之刃（中配）                             |   769.9 |\n",
    "| 10 | 工作细胞                                     |   789.8 |\n",
    "| 11 | 小林家的龙女仆 第二季                        |   828.1 |\n",
    "| 12 | 关于我转生变成史莱姆这档事 转生史莱姆日记    |   829.1 |\n",
    "| 13 | 工作细胞 第二季                              |   836.4 |\n",
    "| 14 | Re：从零开始的异世界生活 第二季 后半         |   838.5 |\n",
    "| 15 | 关于我转生变成史莱姆这档事 第二季            |   883.4 |\n",
    "| 16 | 工作细胞：细胞大作战                         |   913.9 |\n",
    "| 17 | 咒术回战                                     |  1026.8 |\n",
    "| 18 | 鬼灭之刃                                     |  1085.8 |\n",
    "| 19 | 鬼灭之刃 无限列车篇                          |  1146.1 |"
   ]
  },
  {
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   "execution_count": 48,
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     "shell.execute_reply": "2021-11-21T15:36:12.641737Z",
     "shell.execute_reply.started": "2021-11-21T15:36:12.259038Z"
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   "outputs": [
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      "text/plain": [
       "<Figure size 1067.96x660 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# 1. 条形图\n",
    "import pandas as pd\n",
    "import matplotlib as mpl\n",
    "import matplotlib.pyplot as plt\n",
    "from matplotlib.font_manager import FontProperties\n",
    "plt.style.use(\"seaborn\")\n",
    "\n",
    "w, h = mpl.figure.figaspect(0.618)\n",
    "fig = plt.figure(figsize=(w, h), dpi=120)\n",
    "ax = fig.add_subplot(111)\n",
    "y = 2*np.arange(len(data))\n",
    "ax.barh(y, data.iloc[:, 1], align=\"center\", height=1.3, alpha=0.75, edgecolor='k')\n",
    "\n",
    "# 设置柱状图标注\n",
    "# ax.bar_label(rects, padding=3)\n",
    "for i in range(len(data)):\n",
    "    ax.text(data.iloc[i, 1]+3, 2*i-0.2, s=f\"{data.iloc[i, 1]:.1f}\", fontsize=9, verticalalignment=\"center\", horizontalalignment=\"left\")\n",
    "\n",
    "font = FontProperties(fname='data/SIMSUN.TTC')\n",
    "# 设置 y 轴刻度标签\n",
    "ax.set_yticks(y)\n",
    "ax.set_yticklabels(data.iloc[:, 0].values, fontproperties=font)\n",
    "\n",
    "ax.set_title(\"B站11月追番人数 Top 20\", fontproperties=font, fontsize=13)\n",
    "ax.set_xlabel(\"追番人数 (万人)\", fontproperties=font, fontsize=10)\n",
    "ax.set_xlim(500, 1300)\n",
    "fig.tight_layout()\n",
    "\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {
    "execution": {
     "iopub.execute_input": "2021-11-21T15:34:21.059199Z",
     "iopub.status.busy": "2021-11-21T15:34:21.058593Z",
     "iopub.status.idle": "2021-11-21T15:34:21.518275Z",
     "shell.execute_reply": "2021-11-21T15:34:21.517601Z",
     "shell.execute_reply.started": "2021-11-21T15:34:21.059163Z"
    }
   },
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# 2. 频率直方图: Axes.hist()\n",
    "import numpy as np\n",
    "import matplotlib.pyplot as plt\n",
    "plt.rcdefaults()\n",
    "\n",
    "np.random.seed(2223)\n",
    "\n",
    "fig, ax = plt.subplots()\n",
    "x = 30*np.random.randn(10000)\n",
    "mu = x.mean()\n",
    "median = np.median(x)\n",
    "sigma = x.std()\n",
    "textstr = '\\n'.join((\n",
    "    r'$\\mu=%.2f$' % (mu, ),\n",
    "    r'$\\mathrm{median}=%.2f$' % (median, ),\n",
    "    r'$\\sigma=%.2f$' % (sigma, )))\n",
    "\n",
    "ax.hist(x, 50, color=plt.cm.Greens(0.3), edgecolor =plt.cm.Greens(0.9))\n",
    "# these are matplotlib.patch.Patch properties\n",
    "props = dict(boxstyle='round', facecolor='wheat', alpha=0.5)\n",
    "\n",
    "# place a text box in upper left in axes coords\n",
    "ax.text(0.05, 0.95, textstr, transform=ax.transAxes, fontsize=14,\n",
    "        verticalalignment='top', bbox=props)\n",
    "\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {
    "execution": {
     "iopub.execute_input": "2021-11-21T15:33:23.486147Z",
     "iopub.status.busy": "2021-11-21T15:33:23.485189Z",
     "iopub.status.idle": "2021-11-21T15:33:23.677896Z",
     "shell.execute_reply": "2021-11-21T15:33:23.677172Z",
     "shell.execute_reply.started": "2021-11-21T15:33:23.486108Z"
    }
   },
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "x = 10*np.random.randn(1000)\n",
    "plt.hist(x, bins=20,        # 直方图的组距\n",
    "        density=True,       # 设置为频率直方图\n",
    "        cumulative=True,    # 设置为积累直方图\n",
    "        color=plt.cm.Greens(0.3),  # 设置填充色\n",
    "        edgecolor=plt.cm.Greens(0.9))    # 设置直方图的边界色\n",
    "\n",
    "# 设置坐标轴标签和标题\n",
    "plt.title('Cumulative Frequency histogram')\n",
    "plt.xlabel('X Label')\n",
    "plt.ylabel('Cumulative Frequency')\n",
    "\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### 2.2 Polygon-多边形\n",
    "\n",
    "[matplotlib.patches.Polygon](https://matplotlib.org/stable/api/_as_gen/matplotlib.patches.Polygon.html#matplotlib.patches.Polygon) 的基类是 [matplotlib.patches.Patch](https://matplotlib.org/stable/api/_as_gen/matplotlib.patches.Patch.html#matplotlib.patches.Patch)，它的构造函数：\n",
    "\n",
    "```python\n",
    "class matplotlib.patches.Polygon(xy, closed=True, **kwargs)\n",
    "```\n",
    "- xy: array, (N, 2)\n",
    "- close: bool , True, the polygon will be closed so the starting and ending points are the same.\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {
    "execution": {
     "iopub.execute_input": "2021-11-21T15:32:21.199709Z",
     "iopub.status.busy": "2021-11-21T15:32:21.199117Z",
     "iopub.status.idle": "2021-11-21T15:32:21.316671Z",
     "shell.execute_reply": "2021-11-21T15:32:21.316028Z",
     "shell.execute_reply.started": "2021-11-21T15:32:21.199668Z"
    }
   },
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 400x400 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "import numpy as np\n",
    "import math\n",
    "import matplotlib.pyplot as plt\n",
    "import matplotlib.patches as mpatches\n",
    "\n",
    "poly_coords1 = [\n",
    "    (0.3, 0.4), (0.7, 0.4), (0.5, 0.4+0.2*math.sqrt(3))\n",
    "]\n",
    "poly_coords2 = [\n",
    "        (0.3, 0.4+0.4*math.sqrt(3)/3), \n",
    "        (0.7, 0.4+0.4*math.sqrt(3)/3),\n",
    "        (0.5, 0.4-0.2*math.sqrt(3)/3) \n",
    "]\n",
    "fig = plt.figure(figsize=(4, 4))\n",
    "ax = fig.add_subplot(111)\n",
    "poly1 = mpatches.Polygon(xy=poly_coords1)\n",
    "poly1.set_edgecolor('k')\n",
    "ax.add_patch(poly1)\n",
    "poly2 = mpatches.Polygon(xy=poly_coords2)\n",
    "poly2.set_edgecolor('k')\n",
    "ax.add_patch(poly2)\n",
    "\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {
    "execution": {
     "iopub.execute_input": "2021-11-21T15:32:14.346572Z",
     "iopub.status.busy": "2021-11-21T15:32:14.345850Z",
     "iopub.status.idle": "2021-11-21T15:32:14.573518Z",
     "shell.execute_reply": "2021-11-21T15:32:14.572986Z",
     "shell.execute_reply.started": "2021-11-21T15:32:14.346538Z"
    }
   },
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 800x400 with 2 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "import numpy as np\n",
    "import matplotlib.pyplot as plt\n",
    "\n",
    "\n",
    "def koch_snowflake(order, scale=10):\n",
    "    \"\"\"\n",
    "    Return two lists x, y of point coordinates of the Koch snowflake.\n",
    "\n",
    "    Parameters\n",
    "    ----------\n",
    "    order : int\n",
    "        The recursion depth.\n",
    "    scale : float\n",
    "        The extent of the snowflake (edge length of the base triangle).\n",
    "    \"\"\"\n",
    "    def _koch_snowflake_complex(order):\n",
    "        if order == 0:\n",
    "            # initial triangle\n",
    "            angles = np.array([0, 120, 240]) + 90\n",
    "            return scale / np.sqrt(3) * np.exp(np.deg2rad(angles) * 1j)\n",
    "        else:\n",
    "            ZR = 0.5 - 0.5j * np.sqrt(3) / 3\n",
    "\n",
    "            p1 = _koch_snowflake_complex(order - 1)  # start points\n",
    "            p2 = np.roll(p1, shift=-1)  # end points\n",
    "            dp = p2 - p1  # connection vectors\n",
    "\n",
    "            new_points = np.empty(len(p1) * 4, dtype=np.complex128)\n",
    "            new_points[::4] = p1\n",
    "            new_points[1::4] = p1 + dp / 3\n",
    "            new_points[2::4] = p1 + dp * ZR\n",
    "            new_points[3::4] = p1 + dp / 3 * 2\n",
    "            return new_points\n",
    "\n",
    "    points = _koch_snowflake_complex(order)\n",
    "    \n",
    "    x, y = points.real, points.imag\n",
    "    return x, y\n",
    "\n",
    "x, y = koch_snowflake(order=5)\n",
    "\n",
    "fig = plt.figure(figsize=(8, 4))\n",
    "ax = fig.add_subplot(121)\n",
    "ax.axis('equal')\n",
    "poly1, = ax.fill(x, y)\n",
    "poly1.set_facecolor(plt.cm.Oranges(0.3))\n",
    "poly1.set_edgecolor(plt.cm.Oranges(0.9))\n",
    "\n",
    "ax2 = fig.add_subplot(122)\n",
    "x = np.linspace(-2 * np.pi, 2 * np.pi, 1000) \n",
    "y1 = np.sinc(x/2)\n",
    "poly2, = ax2.fill(x, y1)\n",
    "poly2.set_closed(False)\n",
    "poly2.set_facecolor(plt.cm.Greens(0.3))\n",
    "poly2.set_edgecolor(plt.cm.Greens(0.9))\n",
    "\n",
    "plt.show()"
   ]
  }
 ],
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